Publications

Over the last 13 years, at Sandia National Laboratories we have applied the belief/plausibility measure from evidence theory to estimate the uncertainty for numerous safety and security issues for nuclear weapons. For such issues we have significant epistemic uncertainty and are unable to assign probability distributions. We have developed and applied custom software to implement the belief/plausibility measure of uncertainty. For safety issues we perform a quantitative evaluation, and for security issues (e.g., terrorist acts) we use linguistic variables (fuzzy sets) combined with approximate reasoning. We perform the following steps: Train Subject Matter Experts (SMEs) on assignment of evidence Work with SMEs to identify the concern(s): the top-level variable(s) Work with SMEs to identify lower-level variable and functional relationship(s) to the top-level variable(s) Then the SMEs gather their State of Knowledge (SOK) and assign evidence to the lower-level variables. Using this information, we evaluate the variables using custom software and produce an estimate for the top-level variable(s) including uncertainty. We have extended the Kaplan-Garrick risk triplet approach for risk to use the belief/plausibility measure of uncertainty.

Over the last 13 years, at Sandia National Laboratories we have applied the belief/plausibility measure from evidence theory to estimate the uncertainty for numerous safety and security issues for nuclear weapons. For such issues we have significant epistemic uncertainty and are unable to assign probability distributions. We have developed and applied custom software to implement the belief/plausibility measure of uncertainty. For safety issues we perform a quantitative evaluation, and for security issues (e.g., terrorist acts) we use linguistic variables (fuzzy sets) combined with approximate reasoning. We perform the following steps: Train Subject Matter Experts (SMEs) on assignment of evidence Work with SMEs to identify the concern(s): the top-level variable(s) Work with SMEs to identify lower-level variable and functional relationship(s) to the top-level variable(s) Then the SMEs gather their State of Knowledge (SOK) and assign evidence to the lower-level variables. Using this information, we evaluate the variables using custom software and produce an estimate for the top-level variable(s) including uncertainty. We have extended the Kaplan-Garrick risk triplet approach for risk to use the belief/plausibility measure of uncertainty.

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Technical nuclear forensics (TNF) must provide answers to questions of concern to the broader community, including an estimate of uncertainty. There is significant uncertainty associated with post-detonation TNF. The uncertainty consists of a great deal of epistemic (state of knowledge) as well as aleatory (random) uncertainty, and many of the variables of interest are linguistic (words) and not numeric. We provide a process by which TNF experts can structure their process for answering questions and provide an estimate of uncertainty. The process uses belief and plausibility, fuzzy sets, and approximate reasoning.

As the nuclear weapon stockpile ages, there is increased concern about common degradation ultimately leading to common cause failure of multiple weapons that could significantly impact reliability or safety. Current acceptable limits for the reliability and safety of a weapon are based on upper limits on the probability of failure of an individual item, assuming that failures among items are independent. We expanded the current acceptable limits to apply to situations with common cause failure. Then, we developed a simple screening process to quickly assess the importance of observed common degradation for both reliability and safety to determine if further action is necessary. The screening process conservatively assumes that common degradation is common cause failure. For a population with between 100 and 5000 items we applied the screening process and conclude the following. In general, for a reliability requirement specified in the Military Characteristics (MCs) for a specific weapon system, common degradation is of concern if more than 100(1-x)% of the weapons are susceptible to common degradation, where x is the required reliability expressed as a fraction. Common degradation is of concern for the safety of a weapon subsystem if more than 0.1% of the population is susceptible to common degradation. Common degradation is of concern for the safety of a weapon component or overall weapon system if two or more components/weapons in the population are susceptible to degradation. Finally, we developed a technique for detailed evaluation of common degradation leading to common cause failure for situations that are determined to be of concern using the screening process. The detailed evaluation requires that best estimates of common cause and independent failure probabilities be produced. Using these techniques, observed common degradation can be evaluated for effects on reliability and safety.

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Between November 30 and December 11, 2009 an evaluation was performed of the probability of containment failure and the time for cleanup of contamination of the Z machine given failure, for plutonium (Pu) experiments on the Z machine at Sandia National Laboratories (SNL). Due to the unique nature of the problem, there is little quantitative information available for the likelihood of failure of containment components or for the time to cleanup. Information for the evaluation was obtained from Subject Matter Experts (SMEs) at the Z machine facility. The SMEs provided the State of Knowledge (SOK) for the evaluation. There is significant epistemic- or state of knowledge- uncertainty associated with the events that comprise both failure of containment and cleanup. To capture epistemic uncertainty and to allow the SMEs to reason at the fidelity of the SOK, we used the belief/plausibility measure of uncertainty for this evaluation. We quantified two variables: the probability that the Pu containment system fails given a shot on the Z machine, and the time to cleanup Pu contamination in the Z machine given failure of containment. We identified dominant contributors for both the time to cleanup and the probability of containment failure. These results will be used by SNL management to decide the course of action for conducting the Pu experiments on the Z machine.

We recently performed an evaluation of the implications of a reduced stockpile of nuclear weapons for surveillance to support estimates of reliability. We found that one technique developed at Sandia National Laboratories (SNL) under-estimates the required sample size for systems-level testing. For a large population the discrepancy is not important, but for a small population it is important. We found that another technique used by SNL provides the correct required sample size. For systems-level testing of nuclear weapons, samples are selected without replacement, and the hypergeometric probability distribution applies. Both of the SNL techniques focus on samples without defects from sampling without replacement. We generalized the second SNL technique to cases with defects in the sample. We created a computer program in Mathematica to automate the calculation of confidence for reliability. We also evaluated sampling with replacement where the binomial probability distribution applies.

Terrorist acts are intentional and therefore differ significantly from "dumb" random acts that are the subject of most risk analyses. There is significant epistemic (state of knowledge) uncertainty associated with such intentional acts, especially for the likelihood of specific attack scenarios. Also, many of the variables of concern are not numeric and should be treated as purely linguistic (words). Epistemic uncertainty can be addressed using the belief/plausibility measure of uncertainty, an extension of the traditional probability measure of uncertainty. Fuzzy sets can be used to segregate a variable into purely linguistic values. Linguistic variables can be combined using an approximate reasoning rule base to map combinations of fuzzy sets of the constituent variables to fuzzy sets of the resultant variable. We have implemented the mathematics of fuzzy sets, approximate reasoning, and belief/plausibility into Java software tools. The PoolEvidence© software tool combines evidence (pools) from different experts. The LinguisticBelief© software tool evaluates the risk associated with scenarios of concern using the pooled evidence as input. The tools are not limited to the evaluation of terrorist risk; they are useful for evaluating any decision involving significant epistemic uncertainty and linguistic variables. Sandia National Laboratories' analysts have applied the tools to: risk of terrorist acts, security of nuclear materials, cyber security, prediction of movements of plumes of hazardous materials, and issues with nuclear weapons. This paper focuses on evaluating the risk of acts of terrorism. ©2009 IEEE.

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This work provides a comprehensive uncertainty technique to evaluate uncertainty, resulting in a more realistic evaluation of PI, thereby requiring fewer resources to address scenarios and allowing resources to be used across more scenarios. For a given set of dversary resources, two types of uncertainty are associated with PI for a scenario: (1) aleatory (random) uncertainty for detection probabilities and time delays and (2) epistemic (state of knowledge) uncertainty for the adversary resources applied during an attack. Adversary esources consist of attributes (such as equipment and training) and knowledge about the security system; to date, most evaluations have assumed an adversary with very high resources, adding to the conservatism in the evaluation of PI. The aleatory uncertainty in PI is ddressed by assigning probability distributions to detection probabilities and time delays. A numerical sampling technique is used to evaluate PI, addressing the repeated variable dependence in the equation for PI.

The LinguisticBelief%C2%A9 software tool developed by Sandia National Laboratories was applied to provide a qualitative evaluation of the accuracy of various maps that provide information on releases of hazardous material, especially radionuclides. The methodology, %E2%80%9CUncertainty for Qualitative Assessments,%E2%80%9D includes uncertainty in the evaluation. The software tool uses the mathematics of fuzzy sets, approximate reasoning, and the belief/ plausibility measure of uncertainty. SNL worked cooperatively with the Remote Sensing Laboratory (RSL) and the National Atmospheric Release Advisory Center (NARAC) at Lawrence Livermore National Laboratory (LLNL) to develop models for three types of maps for use in this study. SNL and RSL developed the maps for %E2%80%9CAccuracy Plot for Area%E2%80%9D and %E2%80%9CAerial Monitoring System (AMS) Product Confidence%E2%80%9D. SNL and LLNL developed the %E2%80%9CLLNL Model%E2%80%9D. For each of the three maps, experts from RSL and LLNL created a model in the LinguisticBelief software. This report documents the three models and provides evaluations of maps associated with the models, using example data. Future applications will involve applying the models to actual graphs to provide a qualitative evaluation of the accuracy of the maps, including uncertainty, for use by decision makers. A %E2%80%9CQuality Thermometer%E2%80%9D technique was developed to rank-order the quality of a set of maps of a given type. A technique for pooling expert option from different experts was provided using the PoolEvidence%C2%A9 software.

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